Computer Exercises (please select and solve one Computer Exercise out of 3)
C1.
Holding other factors fixed,
where we use the fact that . So is the (ceteris paribus) percentage point change in when increases by one percent.
The null hypothesis is , which means a z% increase in expenditure by A and a z% increase in expenditure by B leaves unchanged. We can equivalently write .
The estimated equation (with standard errors in parentheses below estimates) is
The coefficient on is very significant , as is the coefficient on . The estimates imply that a 10% ceteris paribus increase in spending by candidate A increases the predicted share of the vote going to A by about .61 percentage points. [Recall that, holding other factors fixed, .]
Similarly, a 10% ceteris paribus increase in spending by B reduces by about .66 percentage points. These effects certainly cannot be ignored.
While the coefficients on and are of similar magnitudes (and opposite in sign, as we expect), we do not have the standard error of , which is what we would need to test the hypothesis from part 2).
Write , or . Plugging this into the original equation, and rearranging, gives
When we estimate this equation we obtain ≈ –.532 and se( ) ≈ .533.
The t statistic for the hypothesis in part 2) is –.532/.533 ≈ –1. Therefore, we fail to reject .
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